It sounds as if the motherboard is having a temperature safety shutdown. This occurs when the temperature of the CPU exceeds a certain limit.
First off: Please check your CPU fan, power supply fan, and graphics card fan(if you have a gfx card) that they are working. If not, I would highly recommend replacing the fans or at least cleaning them and attempting to get them started by rotating them manually.
Please enter your BIOS (See Here
for instructions) and navigate to "PC Health Status" - check the entry for the CPU temperature. While in the BIOS there is little strain on the system, but if the temperature is above 40 degrees Celsius in this state it may be prudent to check the fan setting. Also, check if there is a CPU Fan fail warning/CPU warning temperature - on average the limit should not exceed 60-65 degrees Celsius, max. Set any Fan speed or mode settings to maximum if able.
If problem persists, and you are sure the temperature is not too high and/or the CPU fan is working, it may be the power supply itself. It is possible for the power supply to shut itself off in extreme cases such as when a power supply's fan stops working, and the temperature of the power supply rises to an unsafe level. Sometimes the fan will work initially but quit after a certain time. The fan requires replacement if this is the case.
Let the computer sit for a while and check to make sure it is at or near room temperature. Attempt to restart the installation process. When the power is cut, feel where the power supply meets the case to check whether or not it is particularly hot.
Replacement of the power supply's fan should solve that problem. I recommend taking it to a repair shop.
If that is not the problem, a last resort is that the harddrive is overheating and causing a system crash. With the case open, start the computer (mindful to be careful and always touch a large metal object such as the computer case itself before getting your hands near any components to prevent static damage), and wait for it to crash. Place your hand gently on the harddrive. If it is very warm or hot to the touch, most likely the harddrive's actuator arm, circitry, or data plate is malfunctioning and the drive should either be taken to be repaired or replaced.
If none of the components in your computer are particularly hot, please come back with more information on your computer, such as the parts, what you are cd you are booting, any new hardware, etc.